Question: Simplify the following expression: $r = \dfrac{x^2 + 9x + 20}{x + 5} $
Solution: First factor the polynomial in the numerator. $ x^2 + 9x + 20 = (x + 5)(x + 4) $ So we can rewrite the expression as: $r = \dfrac{(x + 5)(x + 4)}{x + 5} $ We can divide the numerator and denominator by $(x + 5)$ on condition that $x \neq -5$ Therefore $r = x + 4; x \neq -5$